Krahn T A, Aronson P S, Weinstein A M
Yale University School of Medicine, New Haven, Connecticut.
Bull Math Biol. 1994 May;56(3):459-90. doi: 10.1007/BF02460467.
Chloride/formate exchange, in parallel with Na+/H+ exchange and nonionic diffusion of H2CO2, has been proposed as a mechanism of electroneutral transcellular Cl- reabsorption by the proximal tubule. However, the measured brush border H2CO2 permeability of the rat proximal tubule is at least an order of magnitude too low to support sufficient H2CO2 recycling. To investigate the possibility that an unstirred layer within the brush border might depress the measured H2CO2 permeability, we constructed a mathematical model of a villous membrane. Axial fluxes along villous and intervillous spaces were specified by Nernst-Planck diffusion equations. Model parameters were set to achieve agreement with ion and water fluxes measured in the rat proximal tubule. The equations were solved numerically to generate steady-state concentration profiles in the villous and intervillous spaces. An apparent brush border H2CO2 permeability was determined by perturbing luminal [H2CO2] and calculating the change in H2CO2 flux. Overall, the ratio of apparent brush border H2CO2 permeability to cell membrane H2CO2 permeability was greater than 90%. Contributing to the small decrease in apparent permeability are finite diffusion coefficients, folding of the membrane, and acidification of the luminal solution. An approximate analysis of this system shows the critical parameters of brush border formate transport to be the actual membrane H2CO2 permeability, and the diffusion coefficients of HCO2- and HCO3-. Nevertheless, decreasing the diffusion coefficients by one order of magnitude failed to depress apparent brush border H2CO2 permeability by more than an additional 25%. We conclude that although permeability is systematically underestimated across a villous membrane, unstirred layer effects in the brush border are still too small to resolve the discrepancy between the measured value of H2CO2 permeability and the value needed to allow recycling.
氯离子/甲酸根交换，与Na⁺/H⁺交换以及H₂CO₂的非离子扩散并行，已被提出作为近端小管电中性跨细胞Cl⁻重吸收的一种机制。然而，所测得的大鼠近端小管刷状缘H₂CO₂通透性至少比支持足够的H₂CO₂循环所需的值低一个数量级。为了研究刷状缘内的一个未搅动层可能会降低所测得的H₂CO₂通透性的可能性，我们构建了一个绒毛膜的数学模型。沿绒毛间隙和绒毛间间隙的轴向通量由能斯特 - 普朗克扩散方程确定。设置模型参数以使其与在大鼠近端小管中测得的离子和水流通量相一致。对这些方程进行数值求解以生成绒毛间隙和绒毛间间隙中的稳态浓度分布。通过扰动管腔[H₂CO₂]并计算H₂CO₂通量的变化来确定表观刷状缘H₂CO₂通透性。总体而言，表观刷状缘H₂CO₂通透性与细胞膜H₂CO₂通透性之比大于90%。有限的扩散系数、膜的折叠以及管腔溶液的酸化导致表观通透性有小幅下降。对该系统的近似分析表明，刷状缘甲酸根转运的关键参数是实际膜H₂CO₂通透性以及HCO₂⁻和HCO₃⁻的扩散系数。然而，将扩散系数降低一个数量级并不会使表观刷状缘H₂CO₂通透性额外降低超过25%。我们得出结论，尽管穿过绒毛膜的通透性被系统地低估了，但刷状缘中的未搅动层效应仍然太小，无法解决所测得的H₂CO₂通透性值与允许循环所需值之间的差异。
